The vector cross product from an algebraic point of view

• Autorzy: Götz Trenkler
• Języki publikacji: EN

Abstrakty

EN

The usual vector cross product of the three-dimensional Euclidian space is considered from an algebraic point of view. It is shown that many proofs, known from analytical geometry, can be distinctly simplified by using the matrix oriented approach. Moreover, by using the concept of generalized matrix inverse, we are able to facilitate the analysis of equations involving vector cross products.

Słowa kluczowe

EN

vector cross product; generalized inverse; Moore-Penrose inverse; linear equations

Kategorie tematyczne

• 15A72: Vector and tensor algebra, theory of invariants

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2001
• Tom: 21
• Numer: 1
• Strony: 67-82

Daty

wydano

2001

otrzymano

1999-10-26

poprawiono

2000-02-11

Twórcy

autor

Götz Trenkler

• Department of Statistics, University of Dortmund, Vogelpothsweg 87, D-44221 Dortmund, Germany

Bibliografia

• [1] A. Ben-Israel, and T.N.E. Greville, Generalized Inverses: Theory and Applications, John Wiley & Sons, New York 1974.
• [2] L.G. Chambers, A Course in Vector Analysis, Chapman and Hall, London 1969.
• [3] B. Hague, An Introduction to Vector Analysis for Physicists and Engineers, (6th edition, revised by D. Martin), Methuen & Science Paperbacks, London 1970.
• [4] T. Lancaster, and M. Tismenetsky, The Theory of Matrices. Academic Press, New York 1985.
• [5] E.A. Milne, Vectorial Mechanics, Methuen & Co. Ltd., London 1965.
• [6] C.R. Rao, and S.K. Mitra, Generalized Inverse of Matrices and its Applications, John Wiley & Sons, New York 1971.
• [7] T.G. Room, The composition of rotations in Euclidean three-space, Amer. Math. Monthly 59 (1952), 688-692.

Identyfikatory

DOI

10.7151/dmgaa.1028